A certain type of integrated circuit is connected to its frame by five wires. Thirty samples of five units each were taken and the pull strength (in grams) of one wire on each unit was measured. The data are presented as follows: Sample Sample Values X R S 10 11 12 13 -234567890122 10.3 9.8 9.7 9.9 10.2 9.9 9.4 10.0 9.4 10.2 9.0 9.9 9.6 9.2 10.6 10.1 10.6 10.3 9.6 9.7 10.8 9.4 9.9 10.1 10.1 10.3 10.1 10.0 9.98 0.6 0.26 9.78 0.8 0.36 9.66 1.6 0.63 10.06 1.0 0.42 10.06 1.4 0.50 9.5 9.8 9.94 0.8 0.30 8.8 9.3 9.9 8.9 9.3 9.24 1.1 0.43 9.4 9.7 9.4 9.9 10.5 9.78 1.1 0.45 9.1 8.9 9.8 9.0 9.3 9.22 0.9 0.36 8.9 9.4 10.6 9.4 8.7 9.40 1.9 0.74 9.0 8.6 9.9 9.6 10.5 9.52 1.9 0.75 9.5 9.2 9.4 9.3 9.6 9.40 0.4 0.16 9.0 9.4 9.7 9.4 8.6 9.22 1.1 0.43 14 9.4 9.2 9.4 9.3 9.7 9.40 0.5 0.19 15 9.4 10.2 9.0 8.8 10.2 9.52 1.4 0.66 16 9.6 9.5 10.0 9.3 9.4 9.56 0.7 0.27 17 10.2 8.8 10.0 10.1 10.1 9.84 1.4 0.59 18 10.4 9.4 9.9 9.4 9.9 9.80 1.0 0.42 19 11.1 10.5 10.6 9.8 9.4 10.28 1.7 0.68 20 9.3 9.9 10.9 9.5 10.6 10.04 1.6 0.69 21 9.5 10.2 9.7 9.4 10.0 9.76 0.8 0.34 22 10.5 10.5 10.1 9.5 10.3 10.18 1.0 0.41 23 9.8 8.9 9.6 9.8 12222233 9.6 9.54 0.9 0.37 24 9.3 9.7 10.3 10.1 9.7 9.82 1.0 0.39 25 10.2 9.6 8.8 9.9 10.2 9.74 1.4 0.58 26 10.8 9.5 10.5 10.5 10.1 10.28 1.3 0.50 27 10.4 9.9 10.1 9.9 10.9 10.24 1.0 0.42 28 11.0 10.8 10.1 9.2 9.9 10.20 1.8 0.72 29 30 10.3 10.0 10.9 10.6 9.9 10.0 10.8 10.6 10.0 11.1 10.40 1.1 0.46 10.44 1.0 0.46 The means are X-9.81, R = 1.14 and 3 = 0.4647. TABLE A.8 Control chart constants Subgroup aved to this PC π Az A3 B3 Ва D3 D. C4 d₂ 2345 1.880 2.659 0.000 3.267 0.000 3.267 0.7979 1.128 1.023 1.954 0.000 2.568 0.000 2.575 0.8862 1.693 0.729 1.628 0.000 2.266 0.000 2.282 0.9213 2.059 5 0.577 1.427 0.000 2.089 0.000 2.114 0.9400 2.326 10 68890 0.483 1.287 0.030 1.970 0.000 2.004 0.9515 2.534 7 0.419 1.182 0.118 1.882 0.076 1.924 0.9594 2.704 0.373 1.099 0.185 1.815 0.136 1.864 0.9650 2.847 0.337 1.032 0.239 1.761 0.184 1.816 0.9693 2.970 0.308 0.975 0.284 1.716 0.223 1.777 0.9727 3.078 1. Compute the LCL limits for the R chart. 2. Compute the UCL limit for the R chart 3. Compute the upper 30 limit for the X-bar chart. 4. Compute the lower 30 limit for the X-bar chart. 5. Calculate the upper lo limit. 6. Calculate the lower 10 limit. 7. Calculate the upper 20 limit. 8. Calculate the lower 20 limit 9. On the basis of the Western Electric rules, is the process mean in control? If not, when is it first detect to be out of control? a. The process is in control. b. The process is out of control for the first time on sample 9. c. The process is out of control for the first time on sample 7. d. The process is out of control in samples 19 and 26 respectively.
A certain type of integrated circuit is connected to its frame by five wires. Thirty samples of five units each were taken and the pull strength (in grams) of one wire on each unit was measured. The data are presented as follows: Sample Sample Values X R S 10 11 12 13 -234567890122 10.3 9.8 9.7 9.9 10.2 9.9 9.4 10.0 9.4 10.2 9.0 9.9 9.6 9.2 10.6 10.1 10.6 10.3 9.6 9.7 10.8 9.4 9.9 10.1 10.1 10.3 10.1 10.0 9.98 0.6 0.26 9.78 0.8 0.36 9.66 1.6 0.63 10.06 1.0 0.42 10.06 1.4 0.50 9.5 9.8 9.94 0.8 0.30 8.8 9.3 9.9 8.9 9.3 9.24 1.1 0.43 9.4 9.7 9.4 9.9 10.5 9.78 1.1 0.45 9.1 8.9 9.8 9.0 9.3 9.22 0.9 0.36 8.9 9.4 10.6 9.4 8.7 9.40 1.9 0.74 9.0 8.6 9.9 9.6 10.5 9.52 1.9 0.75 9.5 9.2 9.4 9.3 9.6 9.40 0.4 0.16 9.0 9.4 9.7 9.4 8.6 9.22 1.1 0.43 14 9.4 9.2 9.4 9.3 9.7 9.40 0.5 0.19 15 9.4 10.2 9.0 8.8 10.2 9.52 1.4 0.66 16 9.6 9.5 10.0 9.3 9.4 9.56 0.7 0.27 17 10.2 8.8 10.0 10.1 10.1 9.84 1.4 0.59 18 10.4 9.4 9.9 9.4 9.9 9.80 1.0 0.42 19 11.1 10.5 10.6 9.8 9.4 10.28 1.7 0.68 20 9.3 9.9 10.9 9.5 10.6 10.04 1.6 0.69 21 9.5 10.2 9.7 9.4 10.0 9.76 0.8 0.34 22 10.5 10.5 10.1 9.5 10.3 10.18 1.0 0.41 23 9.8 8.9 9.6 9.8 12222233 9.6 9.54 0.9 0.37 24 9.3 9.7 10.3 10.1 9.7 9.82 1.0 0.39 25 10.2 9.6 8.8 9.9 10.2 9.74 1.4 0.58 26 10.8 9.5 10.5 10.5 10.1 10.28 1.3 0.50 27 10.4 9.9 10.1 9.9 10.9 10.24 1.0 0.42 28 11.0 10.8 10.1 9.2 9.9 10.20 1.8 0.72 29 30 10.3 10.0 10.9 10.6 9.9 10.0 10.8 10.6 10.0 11.1 10.40 1.1 0.46 10.44 1.0 0.46 The means are X-9.81, R = 1.14 and 3 = 0.4647. TABLE A.8 Control chart constants Subgroup aved to this PC π Az A3 B3 Ва D3 D. C4 d₂ 2345 1.880 2.659 0.000 3.267 0.000 3.267 0.7979 1.128 1.023 1.954 0.000 2.568 0.000 2.575 0.8862 1.693 0.729 1.628 0.000 2.266 0.000 2.282 0.9213 2.059 5 0.577 1.427 0.000 2.089 0.000 2.114 0.9400 2.326 10 68890 0.483 1.287 0.030 1.970 0.000 2.004 0.9515 2.534 7 0.419 1.182 0.118 1.882 0.076 1.924 0.9594 2.704 0.373 1.099 0.185 1.815 0.136 1.864 0.9650 2.847 0.337 1.032 0.239 1.761 0.184 1.816 0.9693 2.970 0.308 0.975 0.284 1.716 0.223 1.777 0.9727 3.078 1. Compute the LCL limits for the R chart. 2. Compute the UCL limit for the R chart 3. Compute the upper 30 limit for the X-bar chart. 4. Compute the lower 30 limit for the X-bar chart. 5. Calculate the upper lo limit. 6. Calculate the lower 10 limit. 7. Calculate the upper 20 limit. 8. Calculate the lower 20 limit 9. On the basis of the Western Electric rules, is the process mean in control? If not, when is it first detect to be out of control? a. The process is in control. b. The process is out of control for the first time on sample 9. c. The process is out of control for the first time on sample 7. d. The process is out of control in samples 19 and 26 respectively.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:A certain type of integrated circuit is connected to its frame by five wires. Thirty samples of five
units each were taken and the pull strength (in grams) of one wire on each unit was measured.
The data are presented as follows:
Sample
Sample Values
X
R
S
10
11
12
13
-234567890122
10.3
9.8 9.7 9.9 10.2
9.9 9.4 10.0 9.4 10.2
9.0 9.9 9.6 9.2 10.6
10.1 10.6 10.3 9.6 9.7
10.8 9.4 9.9 10.1 10.1
10.3 10.1 10.0
9.98
0.6
0.26
9.78
0.8
0.36
9.66
1.6
0.63
10.06
1.0
0.42
10.06
1.4
0.50
9.5 9.8
9.94
0.8
0.30
8.8
9.3 9.9 8.9 9.3
9.24
1.1
0.43
9.4 9.7 9.4
9.9
10.5
9.78
1.1
0.45
9.1
8.9
9.8
9.0 9.3
9.22
0.9
0.36
8.9
9.4
10.6
9.4 8.7
9.40
1.9
0.74
9.0
8.6
9.9
9.6 10.5
9.52
1.9
0.75
9.5
9.2
9.4
9.3 9.6
9.40
0.4
0.16
9.0
9.4
9.7 9.4 8.6
9.22
1.1
0.43
14
9.4
9.2
9.4
9.3 9.7
9.40
0.5
0.19
15
9.4
10.2
9.0 8.8
10.2
9.52
1.4
0.66
16
9.6 9.5
10.0
9.3
9.4
9.56
0.7
0.27
17
10.2 8.8
10.0
10.1
10.1
9.84
1.4
0.59
18
10.4 9.4
9.9 9.4
9.9
9.80
1.0
0.42
19
11.1 10.5 10.6
9.8
9.4
10.28
1.7
0.68
20
9.3 9.9 10.9
9.5 10.6
10.04
1.6
0.69
21
9.5 10.2 9.7
9.4 10.0
9.76
0.8
0.34
22
10.5 10.5 10.1
9.5 10.3
10.18
1.0
0.41
23
9.8
8.9
9.6 9.8
12222233
9.6
9.54
0.9
0.37
24
9.3 9.7
10.3
10.1
9.7
9.82
1.0
0.39
25
10.2
9.6
8.8
9.9
10.2
9.74
1.4
0.58
26
10.8 9.5 10.5
10.5
10.1
10.28
1.3
0.50
27
10.4
9.9 10.1 9.9
10.9
10.24
1.0
0.42
28
11.0 10.8 10.1
9.2 9.9
10.20
1.8
0.72
29
30
10.3 10.0
10.9 10.6 9.9 10.0 10.8
10.6 10.0 11.1
10.40
1.1
0.46
10.44
1.0
0.46
The means are X-9.81, R = 1.14 and 3 = 0.4647.
Transcribed Image Text:TABLE A.8 Control chart constants
Subgroup
aved to this PC
π
Az
A3
B3
Ва
D3
D.
C4
d₂
2345
1.880
2.659
0.000
3.267 0.000
3.267
0.7979
1.128
1.023
1.954
0.000
2.568
0.000
2.575
0.8862 1.693
0.729
1.628
0.000
2.266
0.000
2.282
0.9213
2.059
5
0.577
1.427
0.000
2.089
0.000
2.114
0.9400
2.326
10
68890
0.483
1.287
0.030
1.970
0.000
2.004 0.9515
2.534
7
0.419
1.182
0.118
1.882
0.076
1.924
0.9594
2.704
0.373
1.099
0.185
1.815
0.136
1.864 0.9650
2.847
0.337
1.032
0.239
1.761
0.184
1.816 0.9693
2.970
0.308
0.975
0.284
1.716
0.223
1.777
0.9727 3.078
1. Compute the LCL limits for the R chart.
2. Compute the UCL limit for the R chart
3. Compute the upper 30 limit for the X-bar chart.
4. Compute the lower 30 limit for the X-bar chart.
5. Calculate the upper lo limit.
6. Calculate the lower 10 limit.
7. Calculate the upper 20 limit.
8. Calculate the lower 20 limit
9. On the basis of the Western Electric rules, is the process mean in control? If not, when is
it first detect to be out of control?
a. The process is in control.
b. The process is out of control for the first time on sample 9.
c. The process is out of control for the first time on sample 7.
d. The process is out of control in samples 19 and 26 respectively.
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